arXiv 2306.006112023-06-01gr-qc

非最小导数耦合引力理论中具有任意空间曲率的宇宙学模型

Cosmological models with arbitrary spatial curvature in the theory of gravity with non-minimal derivative coupling

Sergey V. Sushkov, Rafkat Galeev

AI总结：

本文研究非最小导数耦合标量-张量引力中的均匀各向同性宇宙学模型，揭示了任意空间曲率下宇宙可经历动理学暴胀、反弹和循环演化等丰富行为，并给出无需精细调节势的原初暴胀机制。

摘要：

我们研究了标量-张量引力理论中的各向同性和均匀宇宙学场景，其中标量场与曲率的非最小导数耦合由拉格朗日量中的项 $(ζ/H_0^2) G^{μν}\nabla_μϕ\nabla_νϕ$ 给出。一般而言，宇宙学模型由六个无量纲参数决定：耦合参数 $ζ$，以及密度参数 $Ω_0$（宇宙学常数）、$Ω_2$（空间曲率项）、$Ω_3$（非相对论性物质）、$Ω_4$（辐射）、$Ω_6$（标量场项），宇宙演化由修正的弗里德曼方程描述。在 $ζ=0$（无非最小导数耦合）且 $Ω_6=0$（无标量场）的情况下，得到标准 $Λ$CDM 模型；而若 $Ω_6\not=0$，则为含普通标量场的 $Λ$CDM 模型。当标量场具有与曲率的非最小导数耦合，即 $ζ\not=0$ 时，情况发生根本性改变。此时，取决于模型参数：(i) 宇宙存在三种定性不同的初始状态：永恒动理学暴胀、初始奇点和反弹。对于均匀宇宙的所有空间几何类型，反弹都是可能的；(ii) 对于所有空间几何类型，宇宙不可避免地经历原初准德西特（暴胀）时期，此时 $a(t)\propto e^{h_{dS}(H_0t)}$，德西特参数为 $h_{dS}^2={1}/{9ζ}-{8ζΩ_2^3}/{27Ω_6}$。原初暴胀或动理学暴胀的机制由非最小导数耦合提供，且无需精细调节的势；(iii) 存在宇宙演化的循环场景，在标度因子的最小值处发生非奇异反弹，在最大值处出现转折点；(iv) 存在一种提供宇宙学时期更替的自然机制。

英文摘要：

We investigate isotropic and homogeneous cosmological scenarios in the scalar-tensor theory of gravity with non-minimal derivative coupling of a scalar field to the curvature given by the term $(ζ/H_0^2) G^{μν}\nabla_μϕ\nabla_νϕ$ in the Lagrangian. In general, a cosmological model is determined by six dimensionless parameters: the coupling parameter $ζ$, and density parameters $Ω_0$ (cosmological constant), $Ω_2$ (spatial curvature term), $Ω_3$ (non-relativistic matter), $Ω_4$ (radiation), $Ω_6$ (scalar field term), and the universe evolution is described by the modified Friedmann equation. In the case $ζ=0$ (no non-minimal derivative coupling) and $Ω_6=0$ (no scalar field) one has the standard $Λ$CDM-model, while if $Ω_6\not=0$ -- the $Λ$CDM-model with an ordinary scalar field. The situation is crucially changed when the scalar field possesses non-minimal derivative coupling to the curvature, i.e. when $ζ\not=0$. Now, depending on model parameters, (i) There are three qualitatively different initial state of the universe: an eternal kinetic inflation, an initial singularity, and a bounce. The bounce is possible for all types of spatial geometry of the homogeneous universe; (ii) For all types of spatial geometry, the universe goes inevitably through the primary quasi-de Sitter (inflationary) epoch when $a(t)\propto e^{h_{dS}(H_0t)} $ with the de Sitter parameter $h_{dS}^2={1}/{9ζ}-{8ζΩ_2^3}/{27Ω_6}$. The mechanism of primary or kinetic inflation is provided by non-minimal derivative coupling and needs no fine-tuned potential; (iii) There are cyclic scenarios of the universe evolution with the non-singular bounce at a minimal value of the scale factor, and a turning point at the maximal one; (iv) There is a natural mechanism providing a change of cosmological epochs.

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